Optimality Conditions for Higher Order Polyhedral Discrete and Differential Inclusions

DEMİR SAĞLAM S., Mahmudov E.

FILOMAT, cilt.34, sa.13, ss.4533-4553, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 13
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/fil2013533d
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.4533-4553
  • Anahtar Kelimeler: Polyhedral, Higher-order, Differential inclusions, Euler-Lagrange, Transversality, BOUNDARY-VALUE PROBLEM, CONVEX-OPTIMIZATION, 2ND-ORDER DISCRETE, EXISTENCE, SYSTEM
  • İstanbul Üniversitesi Adresli: Evet

Özet

The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.